Obviously it's not a one-to-one thing with the Templars, but I can easily see the Jedi before they bound themselves to the Republic acting as a sort of mercenary fighting force for those individuals/political movements they convince themselves are righteous. I mean, that's sort of what they do already on behalf of the Republic, so it's not that much of a stretch. Either that, or they would control a specific swatch of territory with the Jedi ruling over the commoners by divine right of their Force gifts and occasionally throwing down with their neighbors or rival religious groups. Obviously, the Jedi Order without their ties to the Republic would be a very different beast.

Still, if the Jedi did have those ties to the Republic, I think it would actually make it easier to recruit adults. I mean, the US military has little trouble attracting recruits with the double allure of patriotism and tangible financial benefits.